CUET · MATHS · PYQ PAPER 2023
Which of the following functions is onto?
- A \(f: R \rightarrow R , f(x)=x^2\)
- B \(f: R \rightarrow R , f(x)=x^2+1\)
- C \(f: R \rightarrow R , f(x)=x^2-1\)
- D \(f: R \rightarrow R , f(x)=2 x+1\)
Answer & Solution
Correct Answer
(D) \(f: R \rightarrow R , f(x)=2 x+1\)
Step-by-step Solution
Detailed explanation
Consider \(f(x) = 2x+1\). Let \(y \in R\) (codomain). \(y = 2x+1 \implies x = \frac{y-1}{2}\) For every \(y \in R\), \(x = \frac{y-1}{2}\) is a real number. Range \(= R\). Since Range \(= \text{Codomain}\), \(f: R \rightarrow R , f(x)=2 x+1\) is onto.
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